scholarly journals The involutions-as-principal types/application-as-unification Analogy

10.29007/ntwg ◽  
2018 ◽  
Author(s):  
Alberto Ciaffaglione ◽  
Furio Honsell ◽  
Marina Lenisa ◽  
Ivan Scagnetto
Keyword(s):  
Model Theory ◽  
Open Problem ◽  
Formal Language ◽  
Point Of View ◽  
Combinatory Logic ◽  
Principal Type ◽  
Reversible Computation ◽  
Game Theoretic ◽  
Structural Analogy ◽  
Definition Of

In 2005, S. Abramsky introduced various universal models of computation based on Affine Combinatory Logic, consisting of partial involutions over a suitable formal language of moves, in order to discuss reversible computation in a game-theoretic setting. We investigate Abramsky’s models from the point of view of the model theory of λ-calculus, focusing on the purely linear and affine fragments of Abramsky’s Combinatory Algebras.Our approach stems from realizing a structural analogy, which had not been hitherto pointed out in the literature, between the partial involution interpreting a combinator and the principal type of that term, with respect to a simple types discipline for λ-calculus. This analogy allows for explaining as unification between principal types the somewhat awkward linear application of involutions arising from Geometry of Interaction (GoI).Our approach provides immediately an answer to the open problem, raised by Abram- sky, of characterising those finitely describable partial involutions which are denotations of combinators, in the purely affine fragment. We prove also that the (purely) linear combinatory algebra of partial involutions is a (purely) linear λ-algebra, albeit not a combinatory model, while the (purely) affine combinatory algebra is not. In order to check the complex equations involved in the definition of affine λ-algebra, we implement in Erlang the compilation of λ-terms as involutions, and their execution.

scholarly journals Semantics for Hyperclassical Logic and the Problem of Negation in the Formal Language

2018 ◽  
Vol 16 (3) ◽  
pp. 5-15
Author(s):  
V. V. Tselishchev
Keyword(s):  
Theoretical Model ◽  
Formal Language ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Order Language ◽  
Winning Strategies ◽  
Game Theoretic ◽  
Definition Of ◽  
Game Theoretic Semantics

The application of game-theoretic semantics for first-order logic is based on a certain kind of semantic assumptions, directly related to the asymmetry of the definition of truth and lies as the winning strategies of the Verifier (Abelard) and the Counterfeiter (Eloise). This asymmetry becomes apparent when applying GTS to IFL. The legitimacy of applying GTS when it is transferred to IFL is based on the adequacy of GTS for FOL. But this circumstance is not a reason to believe that one can hope for the same adequacy in the case of IFL. Then the question arises if GTS is a natural semantics for IFL. Apparently, the intuitive understanding of negation in natural language can be explicated in formal languages in various ways, and the result of an incomplete grasp of the concept in these languages can be considered a certain kind of anomalies, in view of the apparent simplicity of the explicated concept. Comparison of the theoretical-model and game theoretic semantics in application to two kinds of language – the first-order language and friendly-independent logic – allows to discover the causes of the anomaly and outline ways to overcome it.

On the Power of Model Theory in Specifying Abstract Data Types and in Capturing Their Recursiveness

1983 ◽  
Vol 6 (2) ◽  
pp. 127-170
Author(s):  
Alberto Bertoni ◽  
Giancarlo Mauri ◽  
Pierangelo Miglioli
Keyword(s):  
Model Theory ◽  
Point Of View ◽  
Necessary Condition ◽  
Abstract Data Type ◽  
Abstract Data Types ◽  
Data Types ◽  
Abstract Data ◽  
Definition Of ◽  
Recursive Data ◽  
Better Than

In this paper a comparative analysis of some algebraic and model-theoretic tools to specify abstract data types is presented: our aim is to show that, in order to capture a quite relevant feature such as the recursiveness of abstract data types, Model Theory works better than Category Theory. To do so, we analyze various notions such as “initiality”, “finality”, “monoinitiality”, “epifinality”, “weak monoinitiality” and “weak epifinality”, both from the point of view of “abstractness” and of “cardinality”, in a general model theoretical frame. For the second aspect, it is shown that only “initiality”, “monoinitiality”, “epifinality” and “weak epifinality” allow us to select countable models (for theories with a countable language), a necessary condition to get recursive data types, while this is not the case for “finality” and “weak monoinitiality”. An extensive analysis is then devoted to the problem of the recursiveness of abstract data types: we provide a formal definition of recursiveness and show that it neither collapses, nor it is incompatible with the “abstractness” requirement. We also show that none of the above quoted categorial notions captures recursiveness. Finally, we consider our own definition of “abstract data type”, based on typically model-theoretic notions, and illustrate the sense according to which it captures recursiveness.

scholarly journals Classical realizability and arithmetical formulæ

2016 ◽  
Vol 27 (6) ◽  
pp. 1068-1107 ◽  
Author(s):  
MAURICIO GUILLERMO ◽  
ÉTIENNE MIQUEY
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Point Of View ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
Theoretic Point ◽  
Winning Strategies ◽  
Game Theoretic ◽  
Definition Of

In this paper, we treat the specification problem in Krivine classical realizability (Krivine 2009Panoramas et synthèses27), in the case of arithmetical formulæ. In the continuity of previous works from Miquel and the first author (Guillermo 2008Jeux de réalisabilité en arithmétique classique, Ph.D. thesis, Université Paris 7; Guillermo and Miquel 2014Mathematical Structures in Computer Science, Epub ahead of print), we characterize the universal realizers of a formula as being the winning strategies for a game (defined according to the formula). In the first sections, we recall the definition of classical realizability, as well as a few technical results. In Section 5, we introduce in more details the specification problem and the intuition of the game-theoretic point of view we adopt later. We first present a game1, that we prove to be adequate and complete if the language contains no instructions ‘quote’ (Krivine 2003Theoretical Computer Science308259–276), using interaction constants to do substitution over execution threads. We then show that as soon as the language contain ‘Quote,’ the game is no more complete, and present a second game2that is both adequate and complete in the general case. In the last Section, we draw attention to a model-theoretic point of view and use our specification result to show that arithmetical formulæ are absolute for realizability models.

Ideal models and some not so ideal problems in the model theory of L(Q)

1978 ◽  
Vol 43 (2) ◽  
pp. 304-321 ◽  
Author(s):  
Kim B. Bruce
Keyword(s):  
Set Theory ◽  
Model Theory ◽  
Point Of View ◽  
Model Completeness ◽  
Intended Meaning ◽  
Generalized Quantifier ◽  
Adequate Definition ◽  
Standard Models ◽  
Definition Of ◽  
Countable Models

It is the purpose of this paper to investigate the model theory of logic with a generalized quantifier; in particular the logic L(Q1) where Q1xφ(x) has the intended meaning “there exist uncountably many x such that φ(x)”. We do this from the point of view that the best way to study what happens in the so-called “ω1-standard” models of L(Q1) is to examine the countable ideal models of L(Q) that satisfy all of the axioms for L(Q1) (see definitions of ω1-standard and ideal models in §1). We believe that this study can be as fruitful for L(Q1) as the study of countable models of ZF has been for set theory.A major problem is formulating an adequate definition of submodel for countable ideal models that is compatible with that for ω1-standard models. Thus we begin the paper by discussing several possible definitions of the notion of submodel. We then adopt a particular definition of submodel and investigate model-completeness in L(Q). We define model-completeness both for ω1-standard models and for countable ideal models and compare the two notions. We also examine elimination of quantifiers, as well as investigating formulas preserved under submodels, again both for ω1-standar d and countable ideal models.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

Dosimetry and optimization in digital radiography based on the contrast-detail resolution

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Wilson Otto Gomes Batista ◽  
Alexandre Gomes De Carvalho
Keyword(s):  
Image Quality ◽  
Inverse Image ◽  
Point Of View ◽  
Complete Analysis ◽  
Portable Devices ◽  
Evaluation Tool ◽  
Air Kerma ◽  
Direct Radiography ◽  
Definition Of ◽  
Entrance Surface Air Kerma

Contrast-detail (C-D) curves are useful in evaluating the radiographic image quality in a global way. The objective of the present study was to obtain the C-D curves and the inverse image quality figure. Both of these parameters were used as an evaluation tool for abdominal and chest imaging protocols. The C-D curves were obtained with the phantom CDRAD 2.0 in computerized radiography and the direct radiography systems (including portable devices). The protocols were 90 and 102 kV in the range of 2 to 20 mAs for the chest and 80 kV in the range of 10 to 80 mAs for the abdomen. The incident air kerma values were evaluated with a solid state sensor. The analysis of these C-D curves help to identify which technique would allow a lower value of the entrance surface air kerma, Ke, while maintaining the image quality from the point of view of C-D detectability. The results showed that the inverse image quality figure, IQFinv, varied little throughout the range of mAs, while the value of Ke varied linearly directly with the mAs values. Also, the complete analysis of the curves indicated that there was an increase in the definition of the details with increasing mAs. It can be concluded that, in the transition phase for the use of the new receptors, it is necessary to evaluate and adjust the practised protocols to ensure, at a minimum, the same levels of the image quality, taking into account the aspects of the radiation protection of the patient.

DIRECTIONS OF ASSOCIATIVE IDENTIFICATION OF PERSONAL NAMES

2019 ◽  
Vol 18 (28) ◽  
pp. 118-128
Author(s):  
Olena Karpenko ◽  
Tetiana Stoianova
Keyword(s):  
Proper Names ◽  
Mental Lexicon ◽  
Point Of View ◽  
Sound Symbolism ◽  
Personal Names ◽  
Communicative Process ◽  
Proper Name ◽  
Definition Of ◽  
Scientific Value ◽  
The Brain

The article is devoted to the study of personal names from a cognitive point of view. The study is based on the cognitive concept that speech actually exists not in the speech, not in linguistic writings and dictionaries, but in consciousness, in the mental lexicon, in the language of the brain. The conditions for identifying personal names can encompass not only the context, encyclopedias, and reference books, but also the sound form of the word. In the communicative process, during a free associative experiment, which included a name and a recipient’s mental lexicon. The recipient was assigned a task to quickly give some association to the name. The aggregate of a certain number of reactions of different recipients forms the associative field of a proper name. The associative experiment creates the best conditions for identifying the lexeme. The definition of a monosemantic personal name primarily includes the search of what it denotes, while during the process of identifying a polysemantic personal name recipients tend have different reactions. Scientific value is posed by the effect of the choice of letters for the name, sound symbolism, etc. The following belong to the generalized forms of identification: usage of a hyperonym; synonyms and periphrases or simple descriptions; associations denoting the whole (name stimulus) by reference to its part (associatives); cognitive structures such as “stimulus — association” and “whole (stimulus) — part (associative)”; lack of adjacency; mysterious associations. The topicality of the study is determined by its perspective to identify the directions of associative identification of proper names, which is one of the branches of cognitive onomastics. The purpose of the study is to identify, review, and highlight the directions of associative identification of proper names; the object of the research is the names in their entirety and variety; its subject is the existence of names in the mental lexicon, which determines the need for singling out the directions for the associative identification of the personal names.

DEFINITION OF THE PUBLIC SECURITY AND ORDERLINESS ENSURING MECHANISM IN UKRAINE

2018 ◽  
Vol 1 (11) ◽  
pp. 155-163
Author(s):  
Marina Aleksandrovna Kalievskaya
Keyword(s):  
Human Rights ◽  
Development Strategy ◽  
State Policy ◽  
The State ◽  
Point Of View ◽  
Public Security ◽  
National Priority ◽  
Institu Tions ◽  
Protection Of Human Rights ◽  
Definition Of

In this article, a model of the mechanism of ensuring public security and orderliness in accordance with the principles and tasks of the relevant institu- tions in public administration, taking into account resources, technologies, mea- sures for the state policy implementation in the spheres of ensuring the protection of human rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order. It was found that ensuring public security and order in Ukraine is a mechanism for the implementation of national goals of state policy in the areas of ensuring the protection of human rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order, by defining tasks according to certain principles. The idea is that if one considers the state policy in the spheres of ensuring the protec- tion of human rights and freedoms, the interests of society and the state, combat- ing crime, maintaining public security and order as a national priority (purpose, task), then the mechanism of ensuring public security and order in Ukraine needs coordination with the state development strategy. From the point of view of the implementation of the state policy in the areas of ensuring the protection of hu- man rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order, the mechanism of ensuring public security and order in Ukraine can be considered as the main system providing intercon- nection such elements as institutions (implementing the specified state policy), resources (human resources, logistical, natural and so on, with the help of which it is possible to implement state policy), technologies (skills, knowledge, means and so on the implementation of state policy), measures (action plans), as well as external (internal) threats.

О вопросах фольклоризма в письменной литературе

2019 ◽  
pp. 31-33
Author(s):  
Суусар Искендерова
Keyword(s):  
Modern Science ◽  
Folk Songs ◽  
Point Of View ◽  
The Past ◽  
Scientific Term ◽  
Literature Culture ◽  
Definition Of ◽  
The Relationship

Аннотация: Исследование проблемы фольклоризма является наиболее актуальной в современной науке о фольклоре. На разных этапах развития художественной литературы для формирования индивидуального творчества писателя особенно значимым становятся фольклорные жанры, сюжетные мотивы и художественные средства. В статье рассматривается связь письменной литературы и фольклора, особенно точка зрения проблеме фольклоризма в прошлом и их анализ. Термин «фольклоризм» начал использоваться советскими исследователями учеными как научный термин еще в 1930-х гг. Термин «фольклоризм» используется в различных сферах культуры, а в этой статье мы будем рассматривать в литературе. Несмотря на то, что на протяжении многих лет этот вопрос изучается литературоведами, фольклористами, все -таки нет единого теоретического определения понятия. Ключевые слова: фольклор, фольклоризм, литература, культура, письменная литература, художественная литература, оседлый народ, пословицы и поговорки, фольклорные песни. Аннотация: Көркөм адабияттын өнүгүүсүнүн ар кайсы баскычтарында сүрөткердин жеке чыгармачылыгынын калыптанышы үчүн фольклордук жанрлар, сюжеттер, мотивдер жана көркөм каражаттар айрыкча мааниге ээ. Макалада жазма адабият менен фольклордук карым-катышы, айрыкча фольклоризм маселеси жөнүндө мурдагы көз караштарга кайрылып, аларга талдоо жүргүзүү менен бирге автор өз байкоолорунда келтирет. “Фольклоризм” деген илимий термин 1930-жылы баштап колдонула баштаган. “Фольклоризм” термини маданияттын түрдүү сфераларында кеңири колдо- нулат, бул жерде адабияттагы колдонулушун каралат. Макалада адабий материал менен фольклордук байланышын терең түшүнүү үчүн адабий фольклоризм маселесинин талаштуу жактары каралат. Түйүндүү сөздөр: фольклор, фольклоризм, адабият, маданият, жазма адабият, көркөм адабият, көчмөн калк, макал-лакап, фольклордук ырлар. Annotation: The study of the problem of folklore is the most relevant in the modern science of folklore. At various stages in the development of fiction, folklore genres, plot motifs, and artistic means become especially significant for the formation of the writer's individual creativity. The article examines the relationship between written literature and folklore, especially the point of view of the problem of folklorism in the past and their analysis. The term "folklorism" began to be used by Soviet scholars as a scientific term back in the 1930s. The term "folklorism" is used in various fields of culture, and in this article we will consider in the literature. Despite the fact that for many years this issue has been studied by literary scholars, folklorists, all the same there is no single theoretical definition of the concept. Keywords: folklore, folklorism, literature, culture, written literature, fiction, settled people, proverbs and sayings, folk songs.

On the Problems of Acts Qualification as Violations of Antimonopoly Legislation in Administrative and Judicial Practice

2020 ◽  
Vol 10 ◽  
pp. 62-69
Author(s):  
К. А. Pisenkо ◽  
Keyword(s):  
Russian Federation ◽  
Point Of View ◽  
Judicial Practice ◽  
Illegal Acts ◽  
The Russian Federation ◽  
Definition Of

The article is devoted to defining the main approaches to classifying acts as violations of аntimonopoly legislation. On administrative and judicial practice discusses current issues and problems of definition of illegal acts, both from the point of view of antimonopoly regulation, and the delineation of antimonopoly violations and violations of other mandatory requirements established by the legislation of the Russian Federation.

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